Silly me. I always thought that juries, not police, convicted defendants and that in arriving at their decisions juries decided whether the weight of the evidence including statements to the police were credible or not.
Why would my comment be at odds with what you thought?
No statements to the Police means less evidence.
If you are guilty, less evidence is good.
If you are not guilty, you can testify on your own behalf, after the prosecution has revealed its entire case.
No statements also mean no contradictions, no retractions, no exaggerations, and no provable lies.
And, in your case, no bizarre comments.